What do Abelian categories form?

@article{Kaledin2022WhatDA,
  title={What do Abelian categories form?},
  author={Dmitry Kaledin},
  journal={Russian Mathematical Surveys},
  year={2022},
  volume={77},
  pages={1 - 45}
}
  • D. Kaledin
  • Published 3 December 2021
  • Mathematics
  • Russian Mathematical Surveys
Given two finitely presentable Abelian categories and , we outline a construction of an Abelian category of functors from to , which has nice 2-categorical properties and provides an explicit model for a stable category of stable functors between the derived categories of and . The construction is absolute, so it makes it possible to recover not only Hochschild cohomology but also Mac Lane cohomology. Bibliography: 29 titles. 
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